Muhammad ibn Mūsā al-Khwārizmī

Muḥammad ibn Mūsā al-Khwārizmī (محمد بن موسی خوارزمی) or al-Khwarizmi (c.780 - 850) was a Persian mathematician, astronomer, astrologer and geographer.

Quotes

• That fondness for science, … that affability and condescension which God shows to the learned, that promptitude with which he protects and supports them in the elucidation of obscurities and in the removal of difficulties, has encouraged me to compose a short work on calculating by al-jabr and al-muqabala , confining it to what is easiest and most useful in arithmetic.
  • As quoted in: Victor J. Katz (2009) A history of mathematics: an introduction. p. 271

• ‘To describe all regions of the earth and to establish all local times would be tedious and unfeasible since, for innumerable times and for boundless regions, the meridians have been recorded with respect to Arin, in such a way that it would not be difficult to determine from this radix by geometrical and arithmetical rules the other places and times... if we are removed in longitude from this (place, namely Arin), then the distance between our place and the locality of Arin must be taken into account’ for calculating the mean positions of planets.
  • Ujjain as the city Arin
  • in the Astronomical Tables of Al-Khwarizmi, first translated by Athelard of Bath into Latin from the Arabic, and later into English by O. Neugebauer
  • quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189

Quotes about al-Khwarizmi

• I have decided first to consider the majority of the authors who up to now have written about [algebra], so that I can fill in what they have missed out. They are very many, and among them Mohammed ibn Musa [Al-Khwarizmi], an Arab, is believed to be the first [...] I believe that the word “algebra” came from him, because some years ago, Brother Luca [Pacioli] of Borgo San Sepolcro of the Minorite order, having set himself the task of writing on this science, as much in Latin as in Italian, said that the word “algebra” was Arabic [...] and that the science came from the Arabs. Many who have written after him have believed and said likewise, but in recent years, a Greek work on this discipline has been discovered in the Library of our Lord in the Vatican, composed by a certain Diophantus of Alexandria, a Greek author [...] Antonio Maria Pazzi and I have translated five books (of the seven) [...] In this work we have found that he cites the Indian authors many times, and thus I have been made aware that this discipline belonged to the Indians before the Arabs.
  • The 16th century Italian mathematician Rafael Bombelli, L’Algebra, published in 1572.
  • quoted in Fauvel, J. and J. Gray. The History of Mathematics: A Reader. Macmillan, 1987. quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189

• As regards algebra, the early Arabs failed to adopt either the Diophantine or the Hindu notations. An examination of [the algebra of Al-Khwarizmi] shows that the exposition was altogether rhetorical, i.e., devoid of all symbolism.
  • Florian Cajori, Cajori, A History of Mathematical Notation, Vol. I, 1993, quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189

• al-Khwārizmī “not having taken algebra from the Greeks,. . . must have either invented it himself, or taken it from the Indians. Of the two, the second appears to me the most probable”
  • Pietro Cossali, who wrote an extensive monograph on the history of algebra quoted in Heeffer, Albrecht. ‘The Reception of Ancient Indian Mathematics by Western Historians’. In Ancient Indian Leaps into Mathematics, edited by B. S. Yadav and Man Mohan, pp. 135-152. Birkhäuser, 2011. quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189

• That he [Al-Khwarizmi] should have borrowed from Diophantus is not at all probable; … It is far more probable that the Arabs received their first knowledge of algebra from the Hindus, who furnished them with the decimal notation of numerals, and with various important points of mathematical and astronomical information.
  • Rosen, Frederic. The Algebra of Mohammed Ben Musa. London: 1831. quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189

• Multicultural education is certainly important, but it should not be about bundling children into preordained faith schools. Awareness of world civilisation and history is necessary. Religious madrasas may take little interest in the fact that when a modern mathematician invokes an "algorithm" to solve a difficult computational problem, she helps to commemorate the secular contributions of Al-Khwarizmi, the great ninth-century Muslim mathematician, from whose name the term algorithm is derived ("algebra" comes from his book, Al Jabr wa-al-Muqabilah). There is no reason at all why old Brits as well as new Brits should not celebrate those grand connections. The world is not a federation of religious ethnicities. Nor, one hopes, is Britain.
  • Amartya Sen, "Solution to cultural confusion is freedom and reason", Financial Times (November 29, 2005)

• Of course the Arabs themselves never laid claim to the invention, always recognizing their indebtedness to the Hindus both for the numeral forms and for the distinguishing feature of place value. Foremost among these writers was the great master of the golden age of Bagdad, one of the first of the Arab writers to collect the mathematical classics of both the East and the West, preserving them and finally passing them on to awakening Europe. This man was Mohammed the Son of Moses, from Khowarezm, or, more after the manner of the Arab, Mohammed ibn Mūsā al-Khowārazmī, a man of great learning and one to whom the world is much indebted for its present knowledge of algebra and of arithmetic. Of him there will often be occasion to speak; and in the arithmetic which he wrote, and of which Adelhard of Bath (c. 1130) may have made the translation or paraphrase, he stated distinctly that the numerals were due to the Hindus. This is as plainly asserted by later Arab writers, even to the present day. Indeed the phrase ilm hindī, "Indian science," is used by them for arithmetic, as [is] also the adjective hindī alone.
  • David Eugene Smith & Louis Charles Karpinski, The Hindu-Arabic Numerals (1911) Ch. I. Early Ideas of Their Origin, pp. 4-5.

• [T]here is a possibility that some of the works ascribed to Sened ibn 'Alī are really works of Al-KhowarazmI, whose name immediately precedes his.
  • David Eugene Smith & Louis Charles Karpinski, The Hindu-Arabic Numerals (1911) Ch. I. Early Ideas of Their Origin, p. 10.